probability

I'm currently trying to generate a spam filter by analyzing a corpus I've amassed. I'm using the wikipedia entry http://en.wikipedia.org/wiki/Bayesian_spam_filtering to develop my classification code. I've implemented code to calculate probability that a message is spam given that it contains a specific word by implementing the following formula from the wiki: My PHP code: public function pSpaminess($word) { $ps = $this->pContentIsSpam(); $ph = $this->pContentIsHam(); $pws = $this->pWordInSpam($word); $pwh = $this->pWordInHam($word); $psw = ($pws * $ps) / ($pws * $ps + $pwh * $ph); return $psw

Given n dice, each of 'a' sides and a sum b, return the number of ways in which the sum b can be obtained. How can you reduce the time complexity and space complexity? This was asked in a Google interview and I am unsure of the answer. This is asking you to find the number of ways to write b as a sum of n positive integers. The answer is the number of compositions of b into n parts, which is (b-1 choose n-1) . Now if we take into account the constraint that the size of the parts is limited to a , the problem gets a little more interesting. I recommend using generating functions for this. The

Given a list of tuples where each tuple consists of a probability and an item I'd like to sample an item according to its probability. For example, give the list [ (.3, 'a'), (.4, 'b'), (.3, 'c')] I'd like to sample 'b' 40% of the time. What's the canonical way of doing this in python? I've looked at the random module which doesn't seem to have an appropriate function and at numpy.random which although it has a multinomial function doesn't seem to return the results in a nice form for this problem. I'm basically looking for something like mnrnd in matlab. Many thanks. Thanks for all the

I am having trouble interpreting the results of a logistic regression. My outcome variable is Decision and is binary (0 or 1, not take or take a product, respectively). My predictor variable is Thoughts and is continuous, can be positive or negative, and is rounded up to the 2nd decimal point. I want to know how the probability of taking the product changes as Thoughts changes. The logistic regression equation is: glm(Decision ~ Thoughts, family = binomial, data = data) According to this model, Thought s has a significant impact on probability of Decision (b = .72, p = .02). To determine the

Through trying to explain the Monty Hall problem to a friend during class yesterday, we ended up coding it in Python to prove that if you always swap, you will win 2/3 times. We came up with this: import random as r #iterations = int(raw_input("How many iterations? >> ")) iterations = 100000 doors = ["goat", "goat", "car"] wins = 0.0 losses = 0.0 for i in range(iterations): n = r.randrange(0,3) choice = doors[n] if n == 0: #print "You chose door 1." #print "Monty opens door 2. There is a goat behind this door." #print "You swapped to door 3." wins += 1 #print "You won a " + doors[2] + "\n"

I have a problem involving a collection of continuous probability distribution functions, most of which are determined empirically (e.g. departure times, transit times). What I need is some way of taking two of these PDFs and doing arithmetic on them. E.g. if I have two values x taken from PDF X, and y taken from PDF Y, I need to get the PDF for (x+y), or any other operation f(x,y). An analytical solution is not possible, so what I'm looking for is some representation of PDFs that allows such things. An obvious (but computationally expensive) solution is monte-carlo: generate lots of values of